You Be "-Illion"!

Earlier this month, the Earth's population passed seven billion. During the summer, the United States' national debt (at least the official debt as calculated by the U.S. Treasury) hit $14 trillion. And in a joke that's been going around for about a decade, various people, including blondes, Texas Aggies, violinists, George W. Bush, and Barack Obama, have learned of the death of several Brazilian skydivers (or Brazilian soldiers in Iraq) and wondered, "How many is a Brazilian?"

The -illion suffix that makes that joke possible originally had no meaning on its own. It was just part of the first and lowest of these number names to be invented, million. According to the Oxford English Dictionary, English borrowed million in the late 1300s from French, which took it from the Italian millione. Since it came from Italian, a reasonable question at this point is why million seems to contain milli-, the Latin root for "thousand," and yet means what it does. That would be the Italian -one suffix, an augmentative that turned the plain mīlle "thousand" into a word that meant a "big thousand"; that is, a thousand thousands. (In fact, according to David Eugene Smith's History of Mathematics (1925), "thousand thousands" was the preferred way to talk about a million in languages other than Italian before million was widely adopted.)

The re-sectioning of milli-one in the original Italian into m-illion in English is an example of "recutting" (as linguists call it), and it happens a lot in languages. Just in English, it's happened with -ology, which is the Greek root –logy with the –o- of roots such as bio- and geo- stuck to it. The adjective alcoholic is transparently composed of the Arabic-derived alcohol plus the suffix -ic, but that didn't stop the -ic from pulling the meaningless -ohol- (sometimes spelled -ahol-) with it to form words like chocoholic, workaholic, and sexaholic. Now we have -aholic as a suffix in its own right, and can playfully form words naming all kinds of addicts. Recutting isn't limited to borrowed words. In his latest book, What Language Is, linguist John McWhorter writes about how lone started off as all one, which merged into alone, which gave rise to lone by removing the ­a-. Summing up, McWhorter writes, "Lone is one with a ripped-off tail end of all hanging on its windshield" (p. 84). Taking a lesson from McWhorter's vivid phrasing, -illion is a fossilized suffix with the headless corpse of milli- hanging on.

However, the strange resemblance of million to words that mean "thousand" is only the beginning of the awkward relationship between -illion words and the numbers they represent. The Latin prefixes are plain to see in billion, trillion, quadrillion, and words for even larger numbers, but what, for example, does the Latin root bi- "two" have to do with the number 109, or tri- "three" with 1012?

It's simple, really. You take the number the Latin prefix denotes, add one, multiply by three, and raise 10 to that power! That is, 103(n + 1), where n = the prefix number. To use quintillion for an example, the quint- means five; five plus one is six; six times three is 18; so a quintillion is 1018. Got it?

All right, so maybe that's not so intuitive. When million, billion, and trillion were coined, the relation was clearer. French mathematician Jehan Adam was the first to use the words bymillion and trimillion in a 1475 manuscript, explaining that the bi-million was a million squared, i.e. (1,000,000)2, and the tri-million was a million cubed: (1,000,000)3. Another French mathematician, Nicolas Chuquet, took these numbers, contracted their names to byllion and trillion, and extended the system all the way up to nonillion before leaving it to his readers to create any further number names that were desired. With the contraction of bi-million and tri-million to billion and trillion, the status of -illion as a suffix was cemented, and it had a clear meaning: a million raised to some power.

As reported in a well-documented Wikipedia article, this simplicity was a casualty of a change in comma usage. Up until the 1600s, commas grouped place-value columns of large numbers into groups of six, instead of the current groups of three. When they began to be used to separate groups of three, some French and Italian scientists began to use billion to refer to the column immediately to the left of the hundred millions (which previously had been called the thousand millions). The other -illion names followed suit, and thus began the separation of the "long scale," with a billion as 1012; and the "short scale," with it as 109. In both scales, a million is still 106, though for the Latin names to follow a consistent pattern in either system, we're going to have to replace it with unillion.

Though the -illion numbers go on higher than the sextillions, octillions, nonillions, and decillions, after about the trillions they become like the obscure names for groups of animals. We're all familiar with, and may have even spoken about, herds of cows, flocks of sheep, maybe even pods of whales. But a murder of crows? A murmuration of starlings? (Actually, murmuration is turning out to be a useful word: It has begun to be used to refer to the groups of thousands of starlings that swoop and arc in hypnotic, synchronized patterns in the fall.) As the OED wryly puts it, these are among "many alleged group terms found in late Middle English glossarial sources, but not otherwise substantiated." The Wikipedia entry on "Names of large numbers" offers a similar sentiment:

Names of larger numbers, however, have a tenuous, artificial existence, rarely found outside definitions, lists, and discussions of the ways in which large numbers are named. Even well-established names like sextillion are rarely used, since in the contexts of science, astronomy, and engineering, where large numbers often occur, numbers are usually written using scientific notation.

Indeed, it's hard enough for the average person to fully grasp the concept of a billion or a trillion, so instead of the words for the larger orders of magnitude, people often prefer to keep things in terms of thousands, millions, and billions. Carl Sagan talked about "billions of billions of stars" instead of "quintillions of stars," though even that got turned into "billions and billions of stars" in the popular culture, turning the minimum estimate into a mere four billion.

If you really want your -illions, though, there are people who are busy naming them for you. The most carefully thought-out system seems to be the Conway-Wechsler extension. Using this chart, I was finally able to find the answer to a question I'd had since I was twelve years old: ten duotrigintillion using the short scale, or ten thousand sedecillion using the long scale, is the -illion-style name for 10100. But I expect most people will continue to call that number by its more familiar name, the googol.

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Neal Whitman blogs at Literal-Minded, where he writes about linguistics in everyday life from the point of view of a husband and father. He taught English as a second language while earning his degree at Ohio State University; has published articles in Language, Journal of Linguistics, and other publications; and writes occasional scripts for the podcast "Grammar Girl's Quick and Dirty Tips for Better Writing."
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Comments from our users:

Thank you Mr. Neal for presenting "-illion"'s history. Most of the facts were unknown to many of us, including many math majors.
I would like to vote for the proposal for the replacement word "unillion." It's thoughtful proposal and the word would promote the idea of unity among diverse society.